An Asymptotic Expansion for the Distribution of the Least Squares Estimator of the Non-Linear Regression Parameter

1977 ◽  
Vol 21 (3) ◽  
pp. 557-570 ◽  
Author(s):  
A. V. Ivanov
Keyword(s):  
Asymptotic Expansion ◽  
Linear Regression ◽  
Least Squares ◽  
Least Squares Estimator ◽  
Regression Parameter ◽  
Non Linear

Least Squares Fitting of Distributions Using Non-Linear Regression.

1980 ◽  
Author(s):  
Mark Heuser ◽  
Paul N. Somerville ◽  
Steven J. Bean
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Least Squares Fitting ◽  
Non Linear

Comparison of three different statistical approaches (non-linear least-squares regression, survival analysis and Bayesian inference) in their usefulness for estimating hydrothermal time models of seed germination

2020 ◽  
Vol 30 (1) ◽  
pp. 64-72 ◽  
Author(s):  
Elena Moltchanova ◽  
Shirin Sharifiamina ◽  
Derrick J. Moot ◽  
Ali Shayanfar ◽  
Mark Bloomberg
Keyword(s):  
Seed Germination ◽  
Linear Regression ◽  
Least Squares ◽  
Time Course ◽  
Efficient Estimation ◽  
Model Parameters ◽  
Least Squares Regression ◽  
Hydrothermal Time ◽  
Linear Least Squares ◽  
Non Linear

AbstractHydrothermal time (HTT) models describe the time course of seed germination for a population of seeds under specific temperature and water potential conditions. The parameters of the HTT model are usually estimated using either a linear regression, non-linear least squares estimation or a generalized linear regression model. There are problems with these approaches, including loss of information, and censoring and lack of independence in the germination data. Model estimation may require optimization, and this can have a heavy computational burden. Here, we compare non-linear regression with survival and Bayesian methods, to estimate HTT models for germination of two clover species. All three methods estimated similar HTT model parameters with similar root mean squared errors. However, the Bayesian approach allowed (1) efficient estimation of model parameters without the need for computation-intensive methods and (2) easy comparison of HTT parameters for the two clover species. HTT models that accounted for a species effect were superior to those that did not. Inspection of credibility intervals and estimated posterior distributions for the Bayesian HTT model shows that it is credible that most HTT model parameters were different for the two clover species, and these differences were consistent with known biological differences between species in their germination behaviour.

Image Texture Classification Based on LS-SVM

2012 ◽  
Vol 182-183 ◽  
pp. 869-872
Author(s):  
Yan Ling Zhao ◽  
Xiao Shi Zheng ◽  
Guang Qi Liu ◽  
Na Li
Keyword(s):  
Support Vector Machine ◽  
Linear Regression ◽  
Least Squares ◽  
Texture Classification ◽  
Energy Ratio ◽  
Image Texture ◽  
Support Vector ◽  
Good Ability ◽  
Non Linear

LS-SVM (Least Squares Support Vector Machine) is simple and has a good ability of non-linear regression. As inputs of LS-SVM, DC-Energy-Ratio and Deviation of image samples are extracted first. Output of LS-SVM is the current texture classification. The results show that LS-SVM classifies images accurately by training the proposed two features.

Confidence Sets for the Coefficients Vector of a Linear Regression Model with Nonspherical Disturbances

1997 ◽  
Vol 13 (3) ◽  
pp. 406-429 ◽  
Author(s):  
Anoop Chaturvedi ◽  
Hikaru Hasegawa ◽  
Ajit Chaturvedi ◽  
Govind Shukla
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Least Squares ◽  
Linear Regression Model ◽  
Generalized Least Squares ◽  
Least Squares Estimator ◽  
Regression Coefficients ◽  
Confidence Sets ◽  
Generalized Least Squares Estimator ◽  
Coverage Probabilities

In this present paper, considering a linear regression model with nonspherical disturbances, improved confidence sets for the regression coefficients vector are developed using the Stein rule estimators. We derive the large-sample approximations for the coverage probabilities and the expected volumes of the confidence sets based on the feasible generalized least-squares estimator and the Stein rule estimator and discuss their ranking.

Reflections on the use of robust and least-squares non-linear regression to model challenge tests conducted in/on food products

2005 ◽  
Vol 104 (2) ◽  
pp. 161-177 ◽  
Author(s):  
N. Miconnet ◽  
A.H. Geeraerd ◽  
J.F. Van Impe ◽  
L. Rosso ◽  
M. Cornu
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Food Products ◽  
Non Linear ◽  
Challenge Tests
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